TY - JOUR
TI - An augmented immersed interface-level set method for Stokes equations with discontinuous viscosity
AU - Li, Zhilin
AU - Lubkin, S.
AU - Wan, X.
T2 - Electronic Journal of Differential Equations, Conference
DA - 2007///
PY - 2007///
VL - 15
SP - 193–210
SN - 1072-6691
ER -
TY - BOOK
TI - Applied Numerical Mathematics for the International Conference on Scientific Computing
A3 - Li, Zhilin
DA - 2007///
PY - 2007///
VL - 57
M3 - Special Issues
PB - American Mathematical Society
ER -
TY - JOUR
TI - An immersed interface method for the Navier-Stokes equations on irregular domains
AU - Li, Zhilin
AU - Lai, Ming-Chih
AU - Ito, Kazufumi
T2 - PAMM
AB - Abstract An augmented method based on a Cartesian grid is proposed for the incompressible Navier Stokes equations on an irregular domain. The irregular domain is embedded into a rectangular one so that a fast Poisson solver can be used in the projection method. Unlike several methods suggested in the literature that set the force strengths as unknowns, which often results an ill‐conditioned linear system, we set the jump in the normal derivative of the velocity as the augmented variable. The new approach improve the condition number of the system for the augmented variable significantly. Using the immersed interface method, we achieve second order accuracy for the velocity. Numerical results and comparisons are given to validate the new method. Some interesting new numerical experiments results are also presented. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
DA - 2007/12//
PY - 2007/12//
DO - 10.1002/pamm.200700758
VL - 7
IS - 1
SP - 1025401-1025402
J2 - Proc. Appl. Math. Mech.
LA - en
OP -
SN - 1617-7061 1617-7061
UR - http://dx.doi.org/10.1002/pamm.200700758
DB - Crossref
ER -
TY - BOOK
TI - Special Issue for the International Conference on Scientific Computing
DA - 2007/5//
PY - 2007/5//
UR - https://www.sciencedirect.com/journal/applied-numerical-mathematics/vol/57/issue/5
ER -
TY - BOOK
TI - Moving Interface Problems and Applications in Fluid Dynamics
DA - 2007///
PY - 2007///
UR - https://books.google.com/books/about/Moving_Interface_Problems_and_Applicatio.html?id=fMYbCAAAQBAJ
ER -
TY - JOUR
TI - Multiscale Considerations in Modeling of Nonlinear Elastomers
AU - Banks, H. T.
AU - Medhin, Negash G.
AU - Pinter, Gabriella A.
T2 - International Journal for Computational Methods in Engineering Science and Mechanics
AB - We present a survey of results from an extended project focused on the understanding of the dynamic behavior of elastomers or filled rubbers. This entailed experimental, modeling, computational and theoretical efforts. Of particular emphasis are the nonlinear and hysteretic aspects of dynamic deformations.
DA - 2007/2/13/
PY - 2007/2/13/
DO - 10.1080/15502280601149346
VL - 8
IS - 2
SP - 53-62
J2 - International Journal for Computational Methods in Engineering Science and Mechanics
LA - en
OP -
SN - 1550-2287 1550-2295
UR - http://dx.doi.org/10.1080/15502280601149346
DB - Crossref
KW - Nonlinear Partial Differential Equations
KW - Computational Methods
KW - Viscoelasticity
KW - Hysteresis
KW - Molecular Dynamics
KW - Multiscale Modeling
ER -
TY - JOUR
TI - Convergence Analysis of the {DIRECT} Algorithm
AU - Finkel, D E
AU - Kelley, C T
DA - 2007///
PY - 2007///
ER -
TY - JOUR
TI - A Case Study in Using Local {I/O} and {GPFS} to Improve Simulation Scalability
T2 - 8th LCI International Conference on High-Performance Clustered Computing
DA - 2007///
PY - 2007///
ER -
TY - JOUR
TI - Analysis of A Scalable Preconditioner for the Wigner-Poisson Equation
AU - Lasater, M.S.
AU - Kelley, C.T.
AU - Salinger, A.
AU - Woolard, D.L.
AU - Recine, G.
AU - Zhao, P.
T2 - International Journal of Pure and Applied Mathematics
DA - 2007///
PY - 2007///
VL - 37
SP - 247–270
ER -
TY - JOUR
TI - Immersed-interface finite-element methods for elliptic interface problems with nonhomogeneous jump conditions
AU - Gong, Y.
AU - Li, B.
AU - Li, Zhilin
T2 - SIAM Journal on Numerical Analysis
AB - In this work, a class of new finite-element methods, called immersed-interface finite-element methods, is developed to solve elliptic interface problems with nonhomogeneous jump conditions. Simple non-body-fitted meshes are used. A single function that satisfies the same nonhomogeneous jump conditions is constructed using a level-set representation of the interface. With such a function, the discontinuities across the interface in the solution and flux are removed, and an equivalent elliptic interface problem with homogeneous jump conditions is formulated. Special finite-element basis functions are constructed for nodal points near the interface to satisfy the homogeneous jump conditions. Error analysis and numerical tests are presented to demonstrate that such methods have an optimal convergence rate. These methods are designed as an efficient component of the finite-element level-set methodology for fast simulation of interface dynamics that does not require remeshing.
DA - 2007///
PY - 2007///
DO - 10.1137/060666482
VL - 46
IS - 1
SP - 472–495
KW - elliptic interface problems
KW - nonhomogeneous jump conditions
KW - immersed-interface finite-element method
KW - level-set functions
KW - error estimates
ER -
TY - JOUR
TI - Explicit solutions for a class of nonlinear PDEs that arise in allocation problems
AU - Dupuis, P.
AU - Zhang, J. X.
T2 - SIAM Journal on Mathematical Analysis
DA - 2007///
PY - 2007///
VL - 39
IS - 5
SP - 1627-1667
ER -
TY - JOUR
TI - Adaptive monitoring and accommodation of nonlinear actuator faults in positive real infinite dimensional systems
AU - Demetriou, Michael A.
AU - Ito, Kazufumi
AU - Smith, Ralph C.
T2 - IEEE TRANSACTIONS ON AUTOMATIC CONTROL
AB - We consider a class of positive real infinite dimensional systems which are subjected to incipient actuator faults. The actuator fault is modeled as a time varying transition from an initial (linear or even nonlinear) map into another unknown nonlinear map at the onset of the fault occurrence. An infinite dimensional adaptive detection observer is utilized to generate a residual signal in order to detect the fault occurrence and to assist in the fault accommodation. This is done via an automated control reconfiguration which utilizes information on the new actuator map and adjusts the controller via a right inverse of the new actuator map. A robust modification is utilized in order to avoid false alarms caused by unmodeled dynamics. An example is included to illustrate the applicability of the proposed detection scheme.
DA - 2007/12//
PY - 2007/12//
DO - 10.1109/TAC.2007.910694
VL - 52
IS - 12
SP - 2332-2338
SN - 1558-2523
KW - actuator faults
KW - distributed parameter systems
KW - fault accommodation
KW - nonlinear actuator dynamics
ER -
TY - JOUR
TI - An adaptive evolutionary algorithm with intelligent mutation local searchers for designing multidrug therapies for HIV
AU - Neri, Ferrante
AU - Toivanen, Jari
AU - Makinen, Raino A. E.
T2 - APPLIED INTELLIGENCE
DA - 2007/12//
PY - 2007/12//
DO - 10.1007/s10489-007-0069-8
VL - 27
IS - 3
SP - 219-235
SN - 1573-7497
ER -
TY - JOUR
TI - Estimation of dynamic rate parameters in insect populations undergoing sublethal exposure to pesticides
AU - Banks, H. T.
AU - Banks, John E.
AU - Dick, Lara K.
AU - Stark, John D.
T2 - BULLETIN OF MATHEMATICAL BIOLOGY
AB - With newer, more environmentally friendly and, subsequently less lethal, pesticides in use, evaluating efficacy of a pesticide now requires more than simply counting deaths after treatment. A discrete, age-structured matrix model that incorporates a species' life history traits (such as birth rate, death rate and fecundity) has previously been used by ecologists. This model will be presented and discussed along with an alternative continuous, age-structured model which offers significant advantage in considering sublethal damage. We use this continuous model to estimate time-dependent mortality parameters in an ordinary least-squares technique. Confidence intervals are given and results from tests for statistical significance of added parameters are presented.
DA - 2007/10//
PY - 2007/10//
DO - 10.1007/s11538-007-9207-z
VL - 69
IS - 7
SP - 2139-2180
SN - 1522-9602
KW - population models
KW - Leslie
KW - Sinko-Streifer
KW - McKendrick-VonForester
KW - time-dependent parameters
ER -
TY - JOUR
TI - Time delay systems with distribution dependent dynamics
AU - Banks, H. T.
AU - Dediu, Sava
AU - Nguyen, Hoan K.
T2 - ANNUAL REVIEWS IN CONTROL
AB - General delay dynamical systems in which uncertainty is present in the form of probability measure dependent dynamics are considered. Several motivating examples arising in biology are discussed. A functional analytic framework for investigating well-posedness (existence, uniqueness and continuous dependence of solutions), inverse problems, sensitivity analysis and approximations of the measures for computational purposes is surveyed.
DA - 2007///
PY - 2007///
DO - 10.1016/j.arcontrol.2007.02.002
VL - 31
IS - 1
SP - 17-26
SN - 1367-5788
KW - inverse dynamics problem
KW - probability distribution function
KW - sensitivity analysis
KW - biomedical systems
ER -
TY - JOUR
TI - Performance of a wavelet-based spectral procedure for steady-state simulation analysis
AU - Lada, E. K.
AU - Wilson, J. R.
AU - Steiger, N. M.
AU - Joines, J. A.
T2 - INFORMS Journal on Computing
AB - A summary and an analysis are given for an experimental performance evaluation of WASSP, an automated wavelet-based spectral method for constructing an approximate confidence interval on the steady-state mean of a simulation output process such that the delivered confidence interval satisfies user-specified requirements on absolute or relative precision as well as coverage probability. The experimentation involved three difficult test problems, each with an output process exhibiting some combination of the following characteristics: a long warm-up period, a persistent autocorrelation structure, or a highly nonnormal marginal distribution. These problems were used to compare the performance of WASSP with that of the Heidelberger-Welch algorithm and ASAP3, two sequential procedures based respectively on the methods of spectral analysis and nonoverlapping batch means. Concerning efficiency (required sample sizes) and robustness against the statistical anomalies commonly encountered in simulation studies, WASSP outperformed the Heidelberger-Welch procedure and compared favorably with ASAP3.
DA - 2007///
PY - 2007///
DO - 10.1287/ijoc.1050.0161
VL - 19
IS - 2
SP - 150–160
KW - simulation
KW - statistical analysis
KW - spectral analysis
KW - steady-state analysis
KW - wavelet analysis
ER -
TY - JOUR
TI - Nonlinear feedback controllers and compensators: a state-dependent Riccati equation approach
AU - Banks, H. T.
AU - Lewis, B. M.
AU - Tran, H. T.
T2 - COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
AB - State-dependent Riccati equation (SDRE) techniques are rapidly emerging as general design and synthesis methods of nonlinear feedback controllers and estimators for a broad class of nonlinear regulator problems. In essence, the SDRE approach involves mimicking standard linear quadratic regulator (LQR) formulation for linear systems. In particular, the technique consists of using direct parameterization to bring the nonlinear system to a linear structure having state-dependent coefficient matrices. Theoretical advances have been made regarding the nonlinear regulator problem and the asymptotic stability properties of the system with full state feedback. However, there have not been any attempts at the theory regarding the asymptotic convergence of the estimator and the compensated system. This paper addresses these two issues as well as discussing numerical methods for approximating the solution to the SDRE. The Taylor series numerical methods works only for a certain class of systems, namely with constant control coefficient matrices, and only in small regions. The interpolation numerical method can be applied globally to a much larger class of systems. Examples will be provided to illustrate the effectiveness and potential of the SDRE technique for the design of nonlinear compensator-based feedback controllers.
DA - 2007/6//
PY - 2007/6//
DO - 10.1007/s10589-007-9015-2
VL - 37
IS - 2
SP - 177-218
SN - 1573-2894
KW - nonlinear feedback control
KW - nonlinear compensator
KW - state-dependent Riccati equations
ER -
TY - JOUR
TI - Stochastic and deterministic models for agricultural production networks
AU - Bai, P.
AU - Banks, H. T.
AU - Dediu, S.
AU - Govan, A. Y.
AU - Last, M.
AU - Lloyd, A. L.
AU - Nguyen, H. K.
AU - Olufsen, M. S.
AU - Rempala, G.
AU - Slenning, B. D.
T2 - Mathematical Biosciences and Engineering
AB - An approach to modeling the impact of disturbances in an agricultural production network is presented. A stochastic model and its approximate deterministic model for averages over sample paths of the stochastic system are developed. Simulations, sensitivity and generalized sensitivity analyses are given. Finally, it is shown how diseases may be introduced into the network and corresponding simulations are discussed.
DA - 2007///
PY - 2007///
DO - 10.3934/mbe.2007.4.373
VL - 4
IS - 3
SP - 373-402
ER -
TY - JOUR
TI - Preface of the special issue of APNUM - International Conference on Scientific Computing in Nanjing, China
AU - Li, Zhilin
AU - Song, Yongzhong
AU - Tang, Tao
T2 - APPLIED NUMERICAL MATHEMATICS
DA - 2007///
PY - 2007///
DO - 10.1016/j.apnum.2006.07.023
VL - 57
IS - 5-7
SP - 473-474
SN - 0168-9274
ER -
TY - JOUR
TI - On a nonlinear size-structured phytoplankton-zooplankton aggregation model
AU - Ackleh, A. S.
AU - Deng, K.
AU - Hu, S. H.
T2 - Dynamics of Continuous, Discrete & Impulsive Systems. Series A, Mathematical Analysis
DA - 2007///
PY - 2007///
VL - 14
IS - 2
SP - 265-285
ER -
TY - JOUR
TI - A two-scale model for an array of AFM's cantilever in the static case
AU - Lenczner, M.
AU - Smith, R. C.
T2 - MATHEMATICAL AND COMPUTER MODELLING
AB - The primary objective of this paper is to present a simplified model for an array of Atomic Force Microscopes (AFMs) operating in static mode. Its derivation is based on the asymptotic theory of thin plates initiated by P. Ciarlet and P. Destuynder and on the two-scale convergence introduced by M. Lenczner which generalizes the theory of G. Nguetseng and G. Allaire. As an example, we investigate in full detail a particular configuration, which leads to a very simple model for the array. Aspects of the theory for this configuration are illustrated through simulation results. Finally the formulation of our theory of two-scale convergence is fully revisited. All the proofs are reformulated in a significantly simpler manner.
DA - 2007/9//
PY - 2007/9//
DO - 10.1016/j.mcm.2006.12.028
VL - 46
IS - 5-6
SP - 776-805
SN - 1872-9479
KW - atomic force microscopy
KW - microsystems arrays
KW - multiscale modeling
KW - homogenization
ER -
TY - JOUR
TI - A study of numerical methods for the level set approach
AU - Gremaud, Pierre A.
AU - Kuster, Christopher M.
AU - Li, Zhilin
T2 - APPLIED NUMERICAL MATHEMATICS
AB - The computation of moving curves by the level set method typically requires reinitializations of the underlying level set function. Two types of reinitialization methods are studied: a high order “PDE” approach and a second order Fast Marching method. Issues related to the efficiency and implementation of both types of methods are discussed, with emphasis on the tube/narrow band implementation and accuracy considerations. The methods are also tested and compared. Fast Marching reinitialization schemes are faster but limited to second order, PDE based reinitialization schemes can easily be made more accurate but are slower, even with a tube/narrow band implementation.
DA - 2007///
PY - 2007///
DO - 10.1016/j.apnum.2006.07.022
VL - 57
IS - 5-7
SP - 837-846
SN - 0168-9274
ER -
TY - JOUR
TI - A fast iterative solver for scattering by elastic objects in layered media
AU - Ito, K.
AU - Toivanen, J.
T2 - APPLIED NUMERICAL MATHEMATICS
AB - We developed a fast iterative solver for computing time-harmonic acoustic waves scattered by an elastic object in layered media. The discretization of the problem was performed using a finite element method with linear elements based on a locally body-fitted uniform triangulation. We used a domain decomposition preconditioner in the iterative solution of the resulting system of linear equations. The preconditioner was based on a cyclic reduction type fast direct solver. The solution procedure reduces GMRES iterates onto a sparse subspace which decreases the storage and computational requirements essentially. The numerical results demonstrate the effectiveness of the proposed approach for two-dimensional domains that are hundreds of wavelengths wide and require the solution of linear systems with several millions of unknowns.
DA - 2007///
PY - 2007///
DO - 10.1016/j.apnum.2006.07.020
VL - 57
IS - 5-7
SP - 811-820
SN - 1873-5460
ER -
TY - JOUR
TI - A comparison of approximation methods for the estimation of probability distributions on parameters
AU - Banks, H. T.
AU - Davis, Jimena L.
T2 - APPLIED NUMERICAL MATHEMATICS
AB - In this paper, we compare two computationally efficient approximation methods for the estimation of growth rate distributions in size-structured population models. After summarizing the underlying theoretical framework, we present several numerical examples as validation of the theory. Furthermore, we compare the results from a spline based approximation method and a delta function based approximation method for the inverse problem involving the estimation of the distributions of growth rates in size-structured mosquitofish populations. Convergence as well as sensitivity of the estimates with respect to noise in the data are discussed for both approximation methods.
DA - 2007///
PY - 2007///
DO - 10.1016/j.apnum.2006.07.016
VL - 57
IS - 5-7
SP - 753-777
SN - 1873-5460
ER -
TY - JOUR
TI - Viscoelasticity in polymers: Phenomenological to molecular mathematical modeling
AU - Banks, H. T.
AU - Luke, N. S.
AU - Samuels, J. R., Jr.
T2 - NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
AB - We report on two recent advances in the modeling of viscoelastic polymers: (i) a new constitutive model that combines the virtual stick-slip continuum “molecular-based” ideas of Johnson and Stacer with the Rouse bead chain ideas; (ii) a two-dimensional version of a model that accounts for stenosis-driven shear wave propagation in biotissue. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 817–831, 2007
DA - 2007/7//
PY - 2007/7//
DO - 10.1002/num.20250
VL - 23
IS - 4
SP - 817-831
SN - 1098-2426
KW - viscoelastic polymers
KW - constitutive models
KW - biotissue
KW - stenosis
KW - shear wave propagation
ER -
TY - JOUR
TI - An augmented approach for Stokes equations with a discontinuous viscosity and singular forces
AU - Li, Zhilin
AU - Ito, Kazufumi
AU - Lai, Ming-Chih
T2 - COMPUTERS & FLUIDS
AB - For Stokes equations with a discontinuous viscosity across an arbitrary interface or/and singular forces along the interface, it is known that the pressure is discontinuous and the velocity is non-smooth. It has been shown that these discontinuities are coupled together, which makes it difficult to obtain accurate numerical solutions. In this paper, a new numerical method that decouples the jump conditions of the fluid variables through two augmented variables has been developed. The GMRES iterative method is used to solve the Schur complement system for the augmented variables that are only defined on the interface. The augmented approach also rescales the Stokes equations in such a way that a fast Poisson solver can be used in each iteration. Numerical tests using examples that have analytic solutions show that the new method has average second order accuracy for the velocity in the infinity norm. An example of a moving interface problem is also presented.
DA - 2007/3//
PY - 2007/3//
DO - 10.1016/j.compfluid.2006.03.003
VL - 36
IS - 3
SP - 622-635
SN - 1879-0747
ER -
TY - JOUR
TI - A stress-dependent hysteresis model for ferroelectric materials
AU - Ball, Brian L.
AU - Smith, Ralph C.
AU - Kim, Sang-Joo
AU - Seelecke, Stefan
T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES
AB - This article addresses the development of a homogenized energy model which characterizes the ferroelastic switching mechanisms inherent to ferroelectric materials in a manner suitable for subsequent transducer and control design. In the first step of the development, we construct Helmholtz and Gibbs energy relations which quantify the potential and electrostatic energy associated with 90 and 180 dipole orientations. Equilibrium relations appropriate for homogeneous materials in the absence or presence of thermal relaxation are respectively determined by minimizing the Gibbs energy or balancing the Gibbs and relative thermal energies using Boltzmann principles. In the final step of the development, stochastic homogenization techniques are employed to construct macroscopic models suitable for nonhomogeneous, polycrystalline compounds. Attributes and limitations of the characterization framework are illustrated through comparison with experimental PLZT data.
DA - 2007/1//
PY - 2007/1//
DO - 10.1177/1045389X07070937
VL - 18
IS - 1
SP - 69-88
SN - 1530-8138
KW - PZT
KW - PLZT
KW - ferroelastic
KW - THUNDER
KW - hysteresis
KW - ferroelectric
KW - Helmholtz
ER -
TY - JOUR
TI - Using mathematical modeling and control to develop structured treatment interruption strategies for HIV infection
AU - Rosenberg, Eric S.
AU - Davidian, Marie
AU - Banks, H. Thomas
T2 - DRUG AND ALCOHOL DEPENDENCE
AB - The goal of this article is to suggest that mathematical models describing biological processes taking place within a patient over time can be used to design adaptive treatment strategies. We demonstrate using the key example of treatment strategies for human immunodeficiency virus type-1 (HIV) infection. Although there has been considerable progress in management of HIV infection using highly active antiretroviral therapies, continuous treatment with these agents involves significant cost and burden, toxicities, development of drug resistance, and problems with adherence; these latter complications are of particular concern in substance-abusing individuals. This has inspired interest in structured or supervised treatment interruption (STI) strategies, which involve cycles of treatment withdrawal and re-initiation. We argue that the most promising STI strategies are adaptive treatment strategies. We then describe how biological mechanisms governing the interaction over time between HIV and a patient's immune system may be represented by mathematical models and how control methods applied to these models can be used to design adaptive STI strategies seeking to maintain long-term suppression of the virus. We advocate that, when such mathematical representations of processes underlying a disease or disorder are available, they can be an important tool for suggesting adaptive treatment strategies for clinical study.
DA - 2007/5//
PY - 2007/5//
DO - 10.1016/j.drugalcdep.2006.12.024
VL - 88
SP - S41-S51
SN - 1879-0046
KW - STI
KW - CD4
KW - HIV dynamics
KW - drug resistance
KW - viral load
ER -
TY - JOUR
TI - Sensitivity of dynamical systems to parameters in a convex subset of a topological vector space
AU - Banks, H. T.
AU - Dediu, S.
AU - Nguyen, H. K.
T2 - Mathematical Biosciences and Engineering
AB - We develop a theory for sensitivity with respect to parameters in a convex subset of a topological vector space of dynamical systems in a Banach space. Specific motivating examples for probability measure dependent differential, partial differential and delay differential equations are given. Schemes that approximate the measures in the Prohorov sense are illustrated with numerical simulations for distributed delay differential equations.
DA - 2007///
PY - 2007///
DO - 10.3934/mbe.2007.4.403
VL - 4
IS - 3
SP - 403-430
ER -
TY - JOUR
TI - Monotone approximation for a nonlinear size and class age structured epidemic model
AU - Banks, H. T.
AU - Bokil, V. A.
AU - Hu, Shuhua
T2 - NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
AB - In this paper, we study a nonautonomous size and class age structured epidemic model with nonlinear and nonlocal boundary conditions. We establish a comparison principle and construct convergent monotone sequences to prove the existence of solutions. Uniqueness of solutions is also established.
DA - 2007/7//
PY - 2007/7//
DO - 10.1016/j.nonrwa.2006.03.008
VL - 8
IS - 3
SP - 834-852
SN - 1468-1218
KW - size and class age structured models
KW - well-posedness
KW - monotone approximations
KW - comparison principle
ER -
TY - JOUR
TI - Solution of time-independent Schrodinger equation by the imaginary time propagation method
AU - Lehtovaara, L.
AU - Toivanen, J.
AU - Eloranta, J.
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - Numerical solution of eigenvalues and eigenvectors of large matrices originating from discretization of linear and non-linear Schrödinger equations using the imaginary time propagation (ITP) method is described. Convergence properties and accuracy of 2nd and 4th order operator-splitting methods for the ITP method are studied using numerical examples. The natural convergence of the method is further accelerated with a new dynamic time step adjustment method. The results show that the ITP method has better scaling with respect to matrix size as compared to the implicitly restarted Lanczos method. An efficient parallel implementation of the ITP method for shared memory computers is also demonstrated.
DA - 2007/1/20/
PY - 2007/1/20/
DO - 10.1016/j.jcp.2006.06.006
VL - 221
IS - 1
SP - 148-157
SN - 1090-2716
KW - imaginary time propagation
KW - Schrodinger equation
KW - Lanczos method
KW - operator-splitting
ER -
TY - JOUR
TI - Mechanism of electric fatigue crack growth in lead zirconate titanate
AU - Westrain, Ilona
AU - Oates, William S.
AU - Lupascu, Doru C.
AU - Roedel, Juergen
AU - Lynch, Christopher S.
T2 - ACTA MATERIALIA
AB - A series of experiments was performed with through-thickness cracks in ferroelectric double cantilever beam (DCB) specimens. Cyclic electric fields of different amplitudes were applied which resulted in cyclic crack propagation perpendicular to the electric field direction. Crack propagation was observed optically and three regimes were identified: a pop-in from a notch, steady-state crack growth and a decrease of the crack growth rate with increasing cycle number. Crack growth only occurred if the applied field exceeded the coercive field strength of the material. Furthermore, the crack extended during each field reversal and the crack growth rate increased with increasing field. Based on the experimental observations, a mechanistic understanding was developed and contrasted with a nonlinear finite element analysis which quantified the stress intensity in the DCB specimens. The driving forces for crack formation at the notch and subsequent fatigue crack growth were computed based on the distribution of residual stresses due to ferroelectric switching. The finite element results are in good agreement with the experimental observations and support the proposed mechanism.
DA - 2007/1//
PY - 2007/1//
DO - 10.1016/j.actamat.2006.08.029
VL - 55
IS - 1
SP - 301-312
SN - 1873-2453
KW - ferroelectricity
KW - fracture
KW - finite element analysis
KW - electroceramics
ER -
TY - JOUR
TI - A dynamic model for induced reactivation of latent virus
AU - Kepler, G. M.
AU - Nguyen, H. K.
AU - Webster-Cyriaque, J.
AU - Banks, H. T.
T2 - JOURNAL OF THEORETICAL BIOLOGY
AB - We develop a deterministic mathematical model to describe reactivation of latent virus by chemical inducers. This model is applied to the reactivation of latent KSHV in BCBL-1 cell cultures with butyrate as the inducing agent. Parameters for the model are first estimated from known properties of the exponentially growing, uninduced cell cultures. Additional parameters that are necessary to describe induction are determined from fits to experimental data from the literature. Our initial model provides good agreement with two independent sets of experimental data, but also points to the need for a new class of experiments which are required for further understanding of the underlying mechanisms.
DA - 2007/2/7/
PY - 2007/2/7/
DO - 10.1016/j.jtbi.2006.08.020
VL - 244
IS - 3
SP - 451-462
SN - 1095-8541
KW - reactivation of latent virus
KW - mathematical model
KW - KSHV
KW - Herpes virus
ER -
TY - JOUR
TI - Model-based robust control design for magnetostrictive transducers operating in hysteretic and nonlinear regimes
AU - Nealis, James M.
AU - Smith, Ralph C.
T2 - IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY
AB - This paper addresses the development of robust control designs for high-performance smart material transducers operating in nonlinear and hysteretic regimes. While developed in the context of a magnetostrictive transducer used for high-speed, high-accuracy milling, the resulting model-based control techniques can be directly extended to systems utilizing piezoceramic or shape memory alloy compounds due to the unified nature of models used to quantify hysteresis and nonlinearities inherent to all of these materials. When developing models and corresponding inverse filters or compensators, significant emphasis is placed on the utilization of the material's physics to provide the accuracy and efficiency required for real-time implementation of resulting model-based control designs. In the material models, this is achieved by combining energy analysis with stochastic homogenization techniques, whereas the efficiency of forward algorithms is combined with monotonicity properties of the material behavior to provide highly efficient inverse algorithms. These inverse filters are then incorporated in H _{2} and H _{infin} theory to provide robust control algorithms capable of providing high-accuracy tracking even though the actuators are operating in nonlinear and hysteretic regimes. Through numerical examples, it is illustrated that the robust designs incorporating inverse compensators can achieve the required tracking tolerance of 1-2 mum for the motivating milling application, whereas robust designs which treat the uncompensated hysteresis and nonlinearities as unmodeled disturbances cannot achieve design specifications
DA - 2007/1//
PY - 2007/1//
DO - 10.1109/TCST.2006.883235
VL - 15
IS - 1
SP - 22-39
SN - 1558-0865
KW - constitutive nonlinearities
KW - distributed parameter systems
KW - hysteresis
KW - inverse filter
KW - magnetostrictive devices
KW - robust control design
ER -
TY - JOUR
TI - Estimation and prediction with HIV-treatment interruption data
AU - Adams, B. M.
AU - Banks, H. T.
AU - Davidian, M.
AU - Rosenberg, E. S.
T2 - BULLETIN OF MATHEMATICAL BIOLOGY
DA - 2007/2//
PY - 2007/2//
DO - 10.1007/s11538-006-9140-6
VL - 69
IS - 2
SP - 563-584
SN - 0092-8240
KW - HIV models
KW - treatment interruptions
KW - censored data
KW - parameter estimation
KW - prediction
ER -
TY - JOUR
TI - Condition estimates for pseudo-arclength continuation
AU - Dickson, K. I.
AU - Kelley, C. T.
AU - Ipsen, I. C. F.
AU - Kevrekidis, I. G.
T2 - SIAM JOURNAL ON NUMERICAL ANALYSIS
AB - We bound the condition number of the Jacobian in pseudo‐arclength continuation problems, and we quantify the effect of this condition number on the linear system solution in a Newton‐GMRES solve. Pseudo‐arclength continuation solves parameter dependent nonlinear equations $G(u,\lambda) = 0$ by introducing a new parameter s, which approximates arclength, and viewing the vector $x = (u,\lambda)$ as a function of s. In this way simple fold singularities can be computed directly by solving a larger system $F(x,s) = 0$ by simple continuation in the new parameter s. It is known that the Jacobian $F_x$ of F with respect to $x=(u,\lambda)$ is nonsingular if the path contains only regular points and simple fold singularities. We introduce a new characterization of simple folds in terms of the singular value decomposition, and we use it to derive a new bound for the norm of $F_x^{-1}$. We also show that the convergence rate of GMRES in a Newton step for $F(x,s)=0$ is essentially the same as that of the original problem $G(u,\lambda)=0$. In particular, we prove that the bounds on the degrees of the minimal polynomials of the Jacobians $F_x$ and $G_u$ differ by at most 2. We illustrate the effectiveness of our bounds with an example from radiative transfer theory.
DA - 2007///
PY - 2007///
DO - 10.1137/060654384
VL - 45
IS - 1
SP - 263-276
SN - 1095-7170
KW - pseudo-arclength continuation
KW - singularity
KW - GMRES
KW - singular vectors
KW - eigenvalues
KW - rank-one update
KW - turning point
KW - simple fold
KW - fold point
KW - limit point
ER -
TY - JOUR
TI - Comparison between stochastic and deterministic selection-mutation models
AU - Ackleh, Azmy S.
AU - Hu, Shuhua
T2 - MATHEMATICAL BIOSCIENCES AND ENGINEERING
AB - We present a deterministic selection-mutation model with a discrete trait variable. We show that for an irreducible selection-mutation matrix in the birth term the deterministic model has a unique interior equilibrium which is globally stable. Thus all subpopulations coexist. In the pure selection case, the outcome is known to be that of competitive exclusion, where the subpopulation with the largest growth-to-mortality ratio will survive and the remaining subpopulations will go extinct. We show that if the selection mutation matrix is reducible, then competitive exclusion or coexistence are possible outcomes. We then develop a stochastic population model based on the deterministic one. We show numerically that the mean behavior of the stochastic model in general agrees with the deterministic one. However, un like the deterministic one, if the differences in the growth-to-mortality ratios are small in the pure selection case, it cannot be determined a priori which subpopulation will have the highest probability of surviving and winning the competition.
DA - 2007/4//
PY - 2007/4//
DO - 10.3934/mbe.2007.4.133
VL - 4
IS - 2
SP - 133-157
SN - 1551-0018
KW - selection-mutation models
KW - competitive exclusion
KW - coexistence
KW - stochastic differential equations
ER -
TY - JOUR
TI - A Finite Difference Method and Analysis for 2D Nonlinear Poisson–Boltzmann Equations
AU - Li, Zhilin
AU - Pao, C. V.
AU - Qiao, Zhonghua
T2 - Journal of Scientific Computing
DA - 2007/1/31/
PY - 2007/1/31/
DO - 10.1007/s10915-005-9019-y
VL - 30
IS - 1
SP - 61–81
SN - 0885-7474 1573-7691
UR - http://dx.doi.org/10.1007/s10915-005-9019-y
KW - nonlinear Poisson-Boltzmann equation
KW - exterior problem
KW - immersed interface method
KW - monotone iterative method
ER -